The effects of treatments may differ between persons with different characteristics. Addressing such treatment heterogeneity is crucial to investigate whether patients with specific characteristics are likely to benefit from a new treatment. The current paper presents a novel Bayesian method for superiority decision-making in the context of randomized controlled trials with multivariate binary responses and heterogeneous treatment effects. The framework is based on three elements: a) Bayesian multivariate logistic regression analysis with a P\'olya-Gamma expansion; b) a transformation procedure to transfer obtained regression coefficients to a more intuitive multivariate probability scale (i.e., success probabilities and the differences between them); and c) a compatible decision procedure for treatment comparison with prespecified decision error rates. Procedures for a priori sample size estimation under a non-informative prior distribution are included. A numerical evaluation demonstrated that decisions based on a priori sample size estimation resulted in anticipated error rates among the trial population as well as subpopulations. Further, average and conditional treatment effect parameters could be estimated unbiasedly when the sample was large enough. Illustration with the International Stroke Trial dataset revealed a trend towards heterogeneous effects among stroke patients: Something that would have remained undetected when analyses were limited to average treatment effects.

翻译：不同特征的患者可能对治疗产生不同反应。解决此类治疗异质性对于探究特定特征患者是否可能从新疗法中获益至关重要。本文提出了一种新颖的贝叶斯方法，用于在具有多元二元响应和异质性治疗效应的随机对照试验中进行优越性决策。该框架基于三个要素：a) 基于Pólya-Gamma扩展的贝叶斯多元逻辑回归分析；b) 将回归系数转换为更直观的多元概率尺度（即成功概率及其差值）的变换程序；c) 符合预设决策错误率的治疗比较兼容决策程序。文中还包含了在无信息先验分布下进行先验样本量估计的方法。数值评估表明，基于先验样本量估计做出的决策在试验人群及子人群中均产生了预期的错误率。此外，当样本量足够大时，平均治疗效应和条件治疗效应参数可实现无偏估计。在国际卒中试验数据集上的应用揭示，卒中患者中存在异质性效应的趋势——若分析仅限于平均治疗效应，这一现象将被忽视。